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In the article we study directional differentiability of maximum functions generated by multivalued mappings. We introduce a new class of Γ-regular multivalued mappings that generalizes the class of mappings, which admit first-order approximation. We also prove directional differentiability of the maximum functions defined on the values of Γ-regular multivalued mappings.
Dedicated to V.F. Demyanov on the occassion of his 65th birthday.
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